Why you should go: It’s an unspoiled spiritual retreat. Mount Kumgang and the surrounding area feature exquisite natural beauty, a famous Zen monastery, and challenging trails for hiking enthusiasts. Nearby Kuryong Falls plunges 242 feet before crashing into a series of lagoons below. A pavilion allows easy viewing of the falls, and mountain paths take travelers more than 5,000 feet up for a stunning panoramic view of the surrounding valleys and the white-sand beaches of the Korean coastline. Enjoy the latter while you can, as electric and barbed-wire fences make access to these beaches rather difficult.

Why you can’t: Because it’s almost impossible. Americans can acquire visas for North Korea, but the only access points are through China and South Korea. Tony Poe, a travel agent based in Little Rock, Arkansas, says that although the North Korean regime has begun to allow U.S. tour groups entry, “you’re basically under quarantine” the entire time. American tourists (of which there have been fewer than 500 since the Korean War ended in 1953) are generally restricted to Pyongyang and the surrounding areas, with Kumgangsan essentially off limits. Straying too far from the tour group is strictly forbidden, and the nonexistent U.S. Embassy and Consulate aren’t going to be of much help if you get into trouble with the Stalinist regime’s notorious secret police.

Baracoa

Location: Cuba’s eastern tip

Why you should go: Baracoa is Cuba’s oldest settlement, founded in 1511 by Spanish conquistadors, and is believed to be near where Christopher Columbus first landed in 1492. Important archaeological sites dot the area, and nearby caves provide visitors an opportunity to view pictographs and ceramic remains of Native American tribes that inhabited the island when Europeans first arrived. Large forts, built in the 18th century to repel pirate attacks, provide breathtaking views of the bay and surrounding forests. The area is also full of sandy beaches, lush vegetation, and waterfalls, not to mention a healthy array of musical, artistic, and cultural happenings.

Why you can’t: Because it is impossible. For a host of reasons—some of which have the last name Castro—U.S. tourist travel to Cuba is thoroughly restricted. Even travel to Cuba through a third country, such as Mexico or Canada, is technically illegal, and violators can face prosecution and a hefty fine of up to $65,000 upon return to the United States. So, although the U.S Guantánamo Bay Naval Base is located in the same province as Baracoa, American travelers who run into problems probably won’t find much sympathy.

Mogadishu’s Beaches

Location: Somalia’s east coast

Why you should go: The beaches that separate Mogadishu from the Indian Ocean rank among the most beautiful stretches of sand in the world, say many of the very few Western travelers who ever venture there. Coral reefs teeming with fish are easily accessible from the shore (although tourists pursuing aquatic leisure should leave all valuables at home in case their boat is hijacked by pirates). Back in Mogadishu, visitors can find virtually anything in the city’s outdoor markets—except peace of mind. A 2004 Economist article noted that hand grenades go for a mere $10, and other popular items include antiaircraft guns and mortars.

Why you can’t: Because a good day in Somalia is the worst day of your life almost anywhere else. The constant state of anarchy, lawlessness, and piracy is usually enough to deter most folks from traveling to Somalia, the world’s third most failed state, according to the 2007 Failed States Index. Michael Sailor of intrepid travel agency Abercrombie & Kent perhaps puts it best when he says that Somalia is “not exactly a top-of-mind recognition for a travel destination.” The U.S. government does not maintain any consular presence in Mogadishu, so an American in trouble is likely to stay there. Most troubling is the fact that with little recognized, governing authority in Somalia, simply identifying which of the seemingly endless string of warlords and criminals has just kidnapped you is an important first step in negotiating your release. Still, the water is lovely.

Persepolis

Location: southern Iran

Why you should go: Declared a UNESCO World Heritage Site in 1979, Persepolis is a vast collection of ruins of columns, palaces, and tombs built by Darius the Great and his son Xerxes I, among other rulers of the Persian Empire. Located 400 miles south of Tehran, Persepolis dates to roughly 517 B.C., when construction began on a city conceived to exhibit the grandeur and power of the Persians. Today, travelers can still see traces of such splendor: The Apadana Palace, the Throne Hall, and the Gate of Xerxes are all popular destinations in this desert city.

Why you can’t: Because, as the U.S. State Department points out in a recent travel warning, “some elements of the Iranian regime remain hostile to the United States.” Visas are hard to come by, as Americans wishing to travel to the theocratic state must have a sponsoring Iranian travel company that first gets approval with the Iranian Ministry of Foreign Affairs. This hurdle makes independent travel essentially impossible, and the wait for a visa can take months. Some U.S. travel agencies can help you make arrangements, but it’s generally up to the individual traveler to trudge through the red tape. Westerners traveling in the southeastern regions of the country, moreover, are susceptible to the armed gangs and contraband smugglers that operate in those areas. Persepolis is somewhat removed from these problem areas, but with relations between the United States and Iran at historic lows, a visit to the Islamic Republic could be a risky move.

Mandalay

Location: Burma

Why you should go: Located far from cyclone-damaged coastal areas, Mandalay’s impressive central palace, Buddhist pagodas, monastery, and other architectural wonders recall the opulence of 19th-century Burma. Mandalay Hill is home to a number of beautifully constructed religious buildings, as well as spectacular views at sunset and sunrise. Best of all, traveling in Burma is incredibly cheap. Tourists can expect to find luxurious lodging in Mandalay’s city center for as little as $40 a night.

Why you can’t: See: Xenophobic, repressive military junta. Although there is a U.S. Embassy in Rangoon, Western travelers still face a litany of dangers in Burma. Because the ruling junta has banned gatherings of more than five people and has recently suppressed peaceful demonstrations with bullets and tear gas, the State Department has advised Americans to stay away from anything that looks political. And with the recent cyclone, even aid workers have had trouble getting visas. Until late May—a full three weeks after Nargis struck the coastal regions—foreign aid workers were denied entry. Indeed, for travel agents, “Burma is pretty much off the radar,” according to Poe. Also, Mandalay’s reputation as the drug trafficking headquarters of Burma might sour some travelers on its charms.